The eurozone's first ever bailout of a debt-laden member country is failing and will need to be renegotiated exactly a year after the €110bn (£96bn) rescue package was agreed for Greece.

Following secret talks in Luxembourg on Friday between Athens and some of the key EU players, it emerged that Greece will not be able to meet the terms of last year's rescue and is hoping to ask the eurozone for more funds.

As Britain made clear it did not want to offer any more support for Greece as part of an EU package or a bilateral loan, investors remain unconvinced of the ability of Athens to sustain its €340bn debt load.

Signalling that his government will struggle to finance itself on the bond markets by next year – which was part of the deal struck with the eurozone and the IMF – the Greek finance minister, George Papaconstantinou, said: "We will either go out to markets or use the recent decision by the EU that allows the European fund to buy Greek bonds. The markets continue to disbelieve in our country."

His trip to Luxembourg had been kept so quiet in Athens that only the prime minister, George Papandreou, knew about the discussions, which were led by Jean-Claude Juncker, the Luxembourg prime minister and president of the group uniting the 17 countries using the single currency. Juncker confirmed that the Greek bailout would need to be renegotiated amid alarmist reports that the country was contemplating reintroducing the drachma.

After the talks – attended by the finance ministers of Germany, France, Italy and Spain as well as Olli Rehn, European monetary affairs commissioner – Juncker said the Greek package needed a "readjustment". Haggling over a new Greek deal is set to dominate the weeks ahead.

EU finance ministers will debate the topic next week and the Germans, in particular, are digging in their heels.

The chancellor, George Osborne, made clear that Britain felt it had done enough to support Greece. He told the Andrew Marr Show: "We certainly don't want to be part of any bailout of Greece, a second bailout. There are some very difficult questions that Greece has to address now because the whole assumption when the eurozone put together a rescue package last year was that Greece could come back into the market next year and borrow. The market is quite sceptical about that happening, and I suspect a lot of my time over the next few weeks is going to be with other European finance ministers and others talking about how we try and help the Greeks get through this situation."

Britain provided a bilateral loan to Ireland last year, but Osborne said: "I can't see us ever writing a cheque directly from the British taxpayer to the Greeks or the Portuguese or indeed anyone else. Ireland was a special case."

Over the weekend, tensions mounted in Ireland after the Irish Central Bank governor was accused of contributing to Ireland's financial crisis by woefully "miscalculating" the extent of losses in the country's banks.

The attack on Patrick Honohan came amid reports that the IMF-European Union and European Central Bank troika had agreed a behind-the-scenes interest rate cut in Ireland's €85bn bailout which could save the country £400m a year.

Experts from the troika are arriving in Athens amid heightened urgency over the handling of the crisis. The Greek government had hoped that the announcement of a mid-term fiscal plan, whose centrepiece is a €50bn privatisation program, would help assuage the criticism of the socialist government's recent performance in implementing a draconian programme of fiscal consolidation.

The normally cool Papaconstantinou appeared uncharacteristically glum after the meeting where sources said Greece had used the occasion to press ahead with its request that eurozone member states soften the terms of the agreement reached on the bailout loans by further extending repayment deadlines.

Adding to the ever growing sense of a government under siege Papandreou slammed critics at the weekend saying: "I call upon everyone in Greece and abroad, and especially in the EU, to leave Greece alone to do its job in peace."